Exact definitions are hard with really fuzzy boundaries. A vampire, demon, fairy, or werewolf set in a secondary world or quasi historic setting might be part of a traditional high, low, historical, or portal, or epic fantasy novel (and all these categories have overlap and debate too), but if it takes place in our "real" and contemporary world it could be part of a paranormal tale or part of an urban fantasy story.
There have been countless threads trying to dissect the difference between UF (or any genre of contemporary fantasy) and paranormal, but I think it comes down to story emphasis and target audience. Paranormal maybe has more emphasis on real-world issues that are altered or enhanced by the addition of the supernatural or fantasy elements (like a bunch of vampires that, for some reason, are hanging out at a suburban high school, posing as normal American teenagers). UF is more focused on the fantasy society or world that exists within, or in parallel, to our own, and on issues central to that world, even if the protagonist moves between the two worlds.
For instance, the Harry Potter books are indisputably fantasy, not paranormal, even though they have werewolves and vampires in them. The emphasis is on the fantasy society and perils that concern it, even if they threaten the mundane world of "muggles" too. Twilight is most commonly categorized as a paranormal romance, however, not a fantasy romance or urban fantasy.
But even that definition gets blurry (as Bella's focus was increasingly on the issues related to Vampire and Werewolf society as the Twilight series progressed). So I think it really comes down to marketing demographics and so on. I've been told that paranormal focuses more on a romance reader demographic, while UF targets readers who are more interested in fantasy first and foremost, though romantic elements can certainly be an important subplot in any fantasy novel.
But there is a fantasy romance subgenre too. So it's complicated, and books can be cross shelved and cross listed.
The general advice people give is to write your story, and you may get more of a sense on where it fits for querying or marketing purposes once it is complete. Genre-savvy beta readers can provide feedback in that respect too.